Normed Rings and Spectral Representation

  • Kôsaku Yosida
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 123)

Abstract

A linear space A over a scalar field (F) is said to be an algebra or a ring over (F), if to each pair of elements x, yA a unique product xyA is defined with the properties:
$$\left. {\begin{array}{*{20}{c}}{\left( {xy} \right)\,z\, = \,x\left( {yz} \right)\,\,\,\left( {associativity} \right),} \\ {x\left( {y\, + \,z} \right)\, = \,xy\, + \,xz\,\,\,\left( {distributivity} \right)} \\ {\alpha \beta \,\left( {xy} \right)\, = \,\left( {\alpha x} \right)\,\left( {\beta y} \right).} \end{array},\,\,\,\,\,\,\,\,\,\,\,} \right\}$$
(1)

Keywords

Hull Tral Topo AvAn BAli 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Kamakura, 247Japan

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